Date of Award
A complex point Z0 is defined to be a member of the famous Mandelbrot set fractal when the iterative process using the function Z2 stays bounded when applied to Z0. We investigate what happens if we change the iterative process so that Z2 is now composed with, for example, a Mobius transformation, indexed on a parameter a. The Mandelbrot set corresponds to a = O. What happens when we change a = 0 to other values, repeating the iterative process and then drawing the sets? Do these Generalized Mandelbrot sets have similar properties to the original Mandelbrot set? This thesis describes some surprising results for these new sets, and it also uses transcendental functions to produce similar generalized sets. Further, it describes the algorithms that were developed and used during the study of each of these sets.
Schlenker, Aaron, "Generalized Mandelbrot Sets" (2014). Undergraduate Honors Thesis Collection. 229.